Some Properties and Uses of Torsional Overlap Integrals
The first diagonalization step in a rho-axis-method treatment of methyl-top internal rotation problems involves finding eigenvalues and eigenvectors of a torsional Hamiltonian, which depends on the rotational projection quantum number K as a parameter. Traditionally the torsional quantum number vt = 0, 1, 2&middot;&middot;&middot;is assigned to eigenfunctions of given K in order of increasing energy. In this paper we propose an alternative labeling scheme, using the torsional quantum number vT, which is based on properties of the K-dependent torsional overlap integrals <vT, K|v'T, K'>. In particular, the quantum number vT is assigned in such a way that torsional wavefunctions |vT, K> vary as slowly as possible when K changes by unity. Roughly speaking, vT = vt for torsional levels below the barrier, whereas vT is more closely related to the free-rotor quantum number for levels above the barrier. Because of the latter fact, we believe vT will in general be a physically more meaningful torsional quantum number for levels above the barrier. The usefulness of <vT, K|v'T, K'> overlap integrals for qualitative prediction of torsion-rotation band intensities and for rationalizing the magnitudes of perturbations involving some excitation of the small-amplitude vibrations in an internal rotor problem is also discussed. Copyright 1998 Academic Press. Copyright 1998Academic Press
Mekhtiev
MA
Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899
Hougen
JT